Pairwise Curve Synchronization for Functional Data

Increasingly, data collected by scientists in different fields are in the form of trajectories or curves. These curves can often be viewed as realizations of a composite process driven by both amplitude and time variation. We consider the situation where functional variation is dominated by time variation, and develop a curve-synchronization method that uses every trajectory in the sample as a reference to obtain pairwise warping functions in a first step. These initial pairwise warping functions are then used to create improved estimators of the underlying individual warping functions in a second step. A truncated averaging process is used to obtain robust estimation of individual warping functions. The method compares well with other available warping approaches and is illustrated with Berkeley growth data and gene expression data for multiple sclerosis.